Should federal courthouse doors be closed to state prisoners?
No, the federal courts should not be closed to state prisoners. The reason for this is that the federal courts are likely the best chance that prisoners have for remedying injustices in their prison conditions.
If the federal courts are closed to prisoners, they will only have state courts to turn to. The state courts may well be unwilling to enforce prisoners' rights because they tend to have elected judges and/or because they will be more attuned to the monetary costs to the state of having to provide better prison conditions.
Therefore, state courts might be unwilling to protect prisoners' constitutional rights, making federal court the prisoners' best hope for protection.
Not only should they continue to be open for redress, the Constitution mandates it.
Article 3 courts are for matters of controversy conerning the constitution, as 28 USC 2254, commonly known as a 2254 Motion can challenge a state conviction on federal constitutional grounds, where a state court of last resort has upheld the persons conviction. The statute is for those held in custody, meaning not out on bail, with minor exceptions to what is defined as custody.
If a state conviction rests soley on state law, and there is no "federal question" involved, even the US Supreme Court can not her ite, rare exceptions.